# Simplify a combination

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I'm trying to simplify the combination defined as : $\binom{n}{\frac{n}{2}}$.

I did some calculations, starting from the factorial formula $\frac{n!}{(\frac{n}{2})!(\frac{n}{2})!}$ and i found this form :

$2^{n}(1-\frac{1}{n})(1-\frac{1}{n-2})(1-\frac{1}{n-4})...$

but i don't know how to continue, can you help me ?

fresh_42
Mentor
2021 Award
but i don't know how to continue, can you help me ?
No, since you haven't said what your goal is. To me ##\binom{n}{\frac{n}{2}}## is already fine.

I want to characterize the behaviour of the formula as n become larger, so i'm trying to simplify it . I'm sorry for the template, next time i'll write it correctly. Thanks for the support

fresh_42
Mentor
2021 Award
I want to characterize the behaviour of the formula as n become larger, so i'm trying to simplify it . I'm sorry for the template, next time i'll write it correctly. Thanks for the support
In this case I'd try where Stirling's approximation would get me.

Ray Vickson